Use Of Steady State Equations For Transient Flow Calculations Available to Purchase

This paper presents an extension and expansion of a novel technique used for calculating the unsteady state behavior of natural gas pipelines. Zhou, Erbar and Maddox (1) presented applications of the technique to straight, horizontal natural gas lines. This paper discusses the application of the procedure to complex pipeline systems and pipeline networks. Discussion of the Method The calculation procedure utilizes standard steady state pressure drop calculations to predict the unsteady state behavior of the line. A typical segment of a gas pipeline is shown in Figure 1. For the steady state conditions, pressure and flow rate for the segment are known. The upset may be either a change in pressure or a change in flow rate. Assume chat a change in discharge flow rate occurs. For the segment of real time chosen as a basis for the calculations, a mass balance is calculated for the pipe segment. Note that the accumulation of gas in the particular segment may be either positive or negative depending on whether the discharge flow rate was decreased or increased in comparison with the steady state flow. From the change in gas inventory, the amount of gas in the segment can be calculated. Using the compressibility of the gas, the temperature and the amount of gas in the section, the pressure at the inlet to the segment can be calculated. This pressure then becomes the new discharge pressure for the next upstream segment of the pipeline. If desired, temperatures can be determined from enthalpy changes and / or heat transfer to/from the gas, the line and surroundings. Applying this procedure to horizontal single gas pipelines has yielded good comparisons with field measurements and other calculation procedures (1). Hannah, et al. (2) have presented data on pipelines under unsteady state conditions. Figure 2 shows the input and output pressures and flow rates for the pipeline identified by Hannah, et al. as "B". In order to simulate this pipeline, inlet and outlet pressures from Figure 2 were fed to the unsteady state pipeline model. Inlet and outlet flow rates were computed. Table I shows a comparison of the inlet and outlet flow rates and percentage errors. The overall absolute percentage deviation for the inlet flow rate is 0.94% and for the outlet flow rate is 1.25%. The 0.94% compares favorably with the overall average deviation of 1.03% for inlet flow rate that Hannah, et al. obtained in their calculations. For more complex piping systems one concern is the necessary number of pressure - flow rate specifications that must be made in order to uniquely define the pipeline system. For a segment of pipe, the number of "degrees of freedom" or variables that must be specified is two. Any combination of input-output flow rate or pressure will define the conditions for either steady or unsteady state flow. In order to test the proposed technique on branched systems, information presented by Hall (3) for a branching system was used.